The present disclosures relate to a device and method for directionally receiving and/or transmitting radio waves.
Signals from a plurality of receiving elements configured as an array can be delayed, or equivalently phase-shifted, and combined (summed) to filter out signal arrivals from particular directions in order to create a set of directional ‘beams’ in physical space. Such beams may be used to improve the reception of signals in an interference background, such as the reception of cellular telephone signals in a radio frequency background dominated by signals originating within the same spatial cell of the mobile telephone network or from adjacent cells.
The same principle works for transmission of direction beams of radio waves as well. In this case, a signal to be directionally transmitted is replicated and phase shifted or delayed, as well as amplitude weighted and fed to the individual transmitting antenna elements, in order to produce desired directional beam characteristics.
For a uniformly sampled array, a fast and efficient form of digital processing that is commonly used to perform beamforming is the well-known ‘Fast-Fourier Transform’ or FFT, a fast version of the Discrete Fourier Transform, or DFT, and known as the ‘Butler Matrix’ in antenna theory.
With DFT/FFT processing, the degree to which frequencies or spatial directions can be resolved, known as the ‘resolving power’ of the system, is normally understood to be limited by the amount of signal observation time (the number of samples times the sampling time interval) in the case of frequency spectrum analysis; or in the case of beam formation, by the aperture size/array dimensions. For example, in the case of a linearly arranged set of receiving elements, an angular beam width (i.e., the spatial resolution for resolving signals arriving from differing directions) for a sufficiently well sampled aperture (spatial sampling no greater than one-half wavelength) is given by the well known ‘diffraction limit’, θ=λ/L, where θ is the beam width, λ is the wavelength corresponding to the incoming signal, and L is the aperture (array) dimension. This limitation often presents a problem to the system designer to whom this limit may appear to be a hard and fast limitation on either system size for a fixed beam resolution requirement or on system resolution where system size is constrained.
In the conventional process of beam formation, weighting factors are often applied to the channel data prior to the DFT transformation for the purposes of reducing spatial response in directions far from the main lobe of the spatial beam pattern. Beam response is reduced on secondary side lobes of the pattern, while the main lobe of the pattern is somewhat widened. See Monzingo and Miller, “Adaptive Arrays”, John Wiley & Sons (1980), p. 274 (Butler Matrix).
In so-called ‘super-gain’ or ‘super-directive’ systems, weighting factors are applied to the channels, prior to the DFT transformation, for the purposes of narrowing the main lobe of the beam, especially in the case where the spacing between receiver elements is less than the required half wavelength. Weighting factors can be chosen in such cases to produce a consequent reduction in beam width (i.e., an increase in resolution), but in general with a loss of system sensitivity and bandwidth. See Doblinger, “Beamforming with Optimized Interpolated Microphone Arrays”, IEEE HSCMA Conference Proceedings (2008), pp 33-37.